Time, t [sec]8。2 8。25 8。3 8。35 8。4 8。45 8。5 8。55

(a) Time, t [sec]

x 105 FFT plot of feed direction forces

0 500 1000 1500 2000 2500

Frequency, /2[Hz]

500 1000 1500 2000 2500

Frequency, /2[Hz]

Fig。 8。  (a) Experimental Fx  plots for stable and unstable conditions at reconfiguration position, y ¼ 451 and (b) corresponding FFTs of the force data。

y ¼ 01。 This is because the FRF plot has a higher magnitude  (4 ~ 106 N/m)  near  the  640 Hz  frequency  for

the y ¼ 451 reconfiguration  position。

The occurrence of chatter was verified from the measured force in the time domain as well as from frequency domain plots。 Figs。 7a and b shows the cutting force  plots  and  FFT  of  the  cutting  force  signal  for  the

y ¼ 01  reconfiguration  position。  It  can  be  seen  from the

force plots, that the cutting force profile is not clearly visible when the cutting was carried out at ap ¼ 5:5 mm, N ¼ 1700 RPM。 This indicates the presence of chatter at these   cutting    conditions。    The    cutting    process    at ap ¼ 5:5 mm, N ¼ 1585 RPM is stable。 The chatter  was also be verified from  the fast  Fourier  transform  (FFT)  of

the force data。 The magnitude of force at the tooth pass frequency is smaller than the magnitude of force at a frequency near one of the natural frequency of the machine structure (i。e。, the chatter frequency), which verifies the existence of chatter。

The cutting experiments did not show very different results for the two reconfiguration positions (Figs。 7 and 8)。 This is because the chatter occurs near the natural frequency 640 Hz, which is expected to come from the spindle–tool–tool holder assembly。 Since this sub-module is not affected during the reconfiguration process, the dynamic contribution due to it would be similar in different reconfiguration   positions。   The   small   difference, which

results in the y ¼ 01 reconfigurable position having    larger

J。 Dhupia et al。 / International Journal of Machine Tools & Manufacture 47 (2007)   326–334 333

500 1000 1500 2000 2500

Spindle Speed, N [RPM]文献综述

Fig。 9。  Analytical lobes generated by structural modes   only。

pockets of instability, was found to be because of higher damping associated with this mode at the y ¼ 01 reconfi-

guration position。 The higher damping in this reconfigura- tion position is the result of the change in distribution of weight at various joints which connect the spindle housing and spindle with the ram plate (Fig。 3)。 If the mode at this 640 Hz frequency is neglected while computing the stability